铝基准晶结构热学与力学性能的分子动力学研究
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摘要
准晶材料是只包含旋转对称性而不具有平移对称性的特殊结构,它具有独特的物理化学性质,已经引起了人们越来越多的关注。利用准晶的硬度特性将其作为合金强化相是它的重要应用,但随着温度变化准晶结构会发生与晶体相结构的可逆性转变。因此了解和预测准晶结构材料的热学与力学性能不仅对于新型准晶材料的发现和制备,而且对于现代工业中的应用都有重要的指导意义。本文应用改进的分析型嵌入原子模型(MAEAM)和分子动力学技术,研究了准晶体系的热学与力学性能,主要包括：二十面体AlNiRh准晶结构转变为密排晶体结构的相变机制以及通过单轴拉伸研究了准晶结构的力学性能。单晶二十面体AlNiRh块体微观结构随温度变化的模拟表明：体系在温度上升过程当中出现了两次结构变化,温度在600 K以下时体系保持稳定,无明显变化,结构中的二十面体只有少量的减少。加温至600 K以上体系向无序化转变,二十面体子结构消失,准晶结构转变为非晶态结构,并且在此过程体系中有过渡相的BCC原子出现。至1100 K以上,体系中出现了较多的FCC与HCP原子,过渡相消失,这与亚稳准晶会在高温下转变为晶态相的结果一致。体系在1800 K发生熔化。对AlNiRh纳米丝在600K以下温度进行单轴拉伸模拟过程表明,与传统晶体的应力应变曲线不同,二十面体准晶的屈服强度较小,且体系的应力—应变曲线明显分为应力上升、应力平稳与应力下降三个阶段,表现出良好的拉伸延性。团簇子结构在应力上升阶段受应力作用结构消失,但是团簇中心Ni原子结构维持稳定,在应变增大过程中有纳米丝断裂于颈缩位置,在拉伸过程当中没有发现滑移现象,也没有晶态原子产生,体系通过塑性断裂机制断裂。并且使用force match方法得到了AlNiCo十次准晶体系的realistic型EAM势函数,应用这种势函数对AlNiCo体系块体拉伸发现体系强度很大,在拉伸过程中有明显滑移现象出现,体系应变量17%以上出现原子层结构破坏,这种结构破坏并且随应变量增大而增大。
Quasicrystal is a new kind of crystal owns Rotational Symmetry but lacks translational symmetry. It has attacted more and more interest nowadays due to its unique properties in physical and chemical applications. Because its incredible hardness, it's usually mixed in other alloys to get them reinforced, but a phase transtition would occur when the critical temperature is reached, so getting to comprehend and predict the thermodynamic and mechanical properities of quasicrystal is not only of great importance and benefit to the discovery and research of new quasicrystal, but also provides a guidance to the wider application of it in the modern industry. In the present thesis, the thermodynamic and mechanical properities of quasicrystal have been investigated with the modified analytic embedded-atom method (MAEAM) and molecular dynamics simulation, including:the mechanism of phase transition from quasicrystal to close-packed crystal phase in icosahedral-AlNiRh quasicrystal and the mechanical properities of quasicrystal performed by uniaxial tension in molecular dynamics simulation. The simulation result of microstructure of the single crystal block AlNiRh according to the temperature reveals that the structure goes through two remarkable change during the heating process. It remains stable when the temperature belows 600K, and there is few icosahedroris lost. When heated above 600K, the microstructure becomes disordered, and the icosahedrons get disappeared. The whole system was transformed into amorphous, with a few atoms which are BCC appears as a transition phase. Plenty of HCP and FCC atoms show up when it's over 1100K and the transition BCC phase disappears. This is consistent with the facts that metastable quasicrystal would transform into crystal phase at high temperature. The block eventually melts at 1800K. The uniaxial tension simulation of AlNiRh nanowire below 600K reveals that icosahedral quasicrystal has a smaller yield strength compared to crystal, and the stress-strain curve is divided in to three stages, which is the rising phase of the stress, the stable phase of stress and the decline phase of stress. The nanowire shows very good tensile ductility. The ico-clusters are damaged in the first stage under the action of stress, but the Ni atoms located at the center of the icosahedral substructure remain stable. The phenomenon of necking is found in the during the tensile process, and neither slidding occurs nor crystal structure is produced. The fracture is due to plastic fracture mechanism. Realistic EAM potential for AlNiCo quasicrystal is gained from the force match method. Uniaxial tension simulation of AlNiCo block is performed, and slip is found when the strain is 10%. The layered structure partly destroyed when stain reached 17%, and ratio of destroyed layers rose with the increase of the strain.
Quasicrystal is a new kind of crystal owns Rotational Symmetry but lacks translational symmetry. It has attacted more and more interest nowadays due to its unique properties in physical and chemical applications. Because its incredible hardness, it's usually mixed in other alloys to get them reinforced, but a phase transtition would occur when the critical temperature is reached, so getting to comprehend and predict the thermodynamic and mechanical properities of quasicrystal is not only of great importance and benefit to the discovery and research of new quasicrystal, but also provides a guidance to the wider application of it in the modern industry. In the present thesis, the thermodynamic and mechanical properities of quasicrystal have been investigated with the modified analytic embedded-atom method (MAEAM) and molecular dynamics simulation, including:the mechanism of phase transition from quasicrystal to close-packed crystal phase in icosahedral-AlNiRh quasicrystal and the mechanical properities of quasicrystal performed by uniaxial tension in molecular dynamics simulation. The simulation result of microstructure of the single crystal block AlNiRh according to the temperature reveals that the structure goes through two remarkable change during the heating process. It remains stable when the temperature belows 600K, and there is few icosahedroris lost. When heated above 600K, the microstructure becomes disordered, and the icosahedrons get disappeared. The whole system was transformed into amorphous, with a few atoms which are BCC appears as a transition phase. Plenty of HCP and FCC atoms show up when it's over 1100K and the transition BCC phase disappears. This is consistent with the facts that metastable quasicrystal would transform into crystal phase at high temperature. The block eventually melts at 1800K. The uniaxial tension simulation of AlNiRh nanowire below 600K reveals that icosahedral quasicrystal has a smaller yield strength compared to crystal, and the stress-strain curve is divided in to three stages, which is the rising phase of the stress, the stable phase of stress and the decline phase of stress. The nanowire shows very good tensile ductility. The ico-clusters are damaged in the first stage under the action of stress, but the Ni atoms located at the center of the icosahedral substructure remain stable. The phenomenon of necking is found in the during the tensile process, and neither slidding occurs nor crystal structure is produced. The fracture is due to plastic fracture mechanism. Realistic EAM potential for AlNiCo quasicrystal is gained from the force match method. Uniaxial tension simulation of AlNiCo block is performed, and slip is found when the strain is 10%. The layered structure partly destroyed when stain reached 17%, and ratio of destroyed layers rose with the increase of the strain.
引文
[1]Shechtman D, Blech I, Gratias D, et al. Metallic phase with long-ranged orientational order and no translational symmetry. Physical Review Letters, 1984,53(20):1951-1954
[2]Levine D, Steinhardt P J. Quasicrystals:A new class of ordered structures. Physical Review Letters,1984,53(26):2477-2480
[3]Penrose R. Pentaplexity. Eureka,1978,39:16-22
[4]Penrose R. The role of aesthetics in pure and applied mathematical research. Bulletin of the Institute of Mathematics and its Applications,1974,10:266-271
[5]Elser V. Indexing problems in quasicrystal diffraction. Physical Review B,1985, 32(8):4892-4898
[6]Katz A, Duneau M. Quasiperiodic patterns and icosahedral symmetry. Journal of Physical France.1986,47(2):181-196
[7]Gahler F, Gummelt P, Ben-Abraham S I. Generation of quasiperiodic order by maximal cluster covering, in Coverings of Discrete Quasiperiodic Sets:Theory and Applications to Quasicrystals. Berlin:Springer,2002,63-93
[8]Ben-Abraham S I, Gummelt P, Luck R, et al. Dodecagonal tilings almost covered by a single cluster. Ferroelectrics,2001,250(1-4):313-316
[9]Gahler F, Luck R, Ben-Abraham S I, et al. Dodecagonal tilings as maximal cluster coverings. Ferroelectrics,2001,250(1-4):335-338
[10]Gummelt P, Bandt C. A cluster approach to random Penrose tilings. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing,2000,294-296:250-253
[11]Puellmann K, Gummelt I, Kadar J, et al. Apoptosis of normal and G-CSF induced cells:Influences of pentoxifylline and amifostine. Journal of Leukocyte Biology,1998,48:178-183
[12]Gummelt P. Penrose tilings as coverings of congruent decagons. Geometriae Dedicata,1996,62(1):1-17
[13]Schechtman D, Blech I A. The microstructure of rapidly solidified A16Mn. Metallurgical and Materials Transactions A,1985,16(6):1005-1012
[14]Stephens P W, Goldman A I. Sharp Diffraction Maxima from an Icosahedral Glass. Physical Review Letters,1986,56(17):1168-1171
[15]Widom M, Strandgurg K, Swenden R H. Quasicrystal equilibrium state. Physical Review Letters,1987,58(7):706-709
[16]Janssen T. In Quasicrystals, Proceedings of the Adriatico Research Conference. Edited by Jaric and S. Lundquist. Singapore:World Scientific,1990,337-341
[17]Elser V. Comment on Quasicrystals:A New Class of Ordered Structures. Physical Review Letters,1985,54(15):1730-1733
[18]Strandburg K. Random-tiling quasicrystal. Physical Review B,1989,40(9): 6071-6084
[19]Pauling L. Apparent icosaedral symmetry is due to directed multiple twinning of cubic crystals. Nature,1985,317:512-514
[20]Pauling L. So-called icosahedral and decagonal quasicrysatls are twins of an 820-atom cubic crystal. Physical Review Letters,1987,58(4):365-368
[21]Henley C, Elser V. Quasicrystal structure of (Al,Zn)49Mg32. Philosophical Magazine B,1986,53(3):L59-L66
[22]Guyot P, Audier M. A quasicrystal structure model for AI-Mn. Philosophical Magazine B,1985,52(1):L15-L19
[23]Audier M, Guyot P. A perfect icosahedral atomic structure:A two-unit-cell and four-zonohedra description. Philosophical Magazine Letters,1988,58(1):17-23
[24]Elser V. XVth International Colloquiumon Groupn Theoretical Methods in Physics, edited by R. Gilmore. Singapore:World Scientific,1987,330-334
[25]Henley C L. Random tilings with quasicrystal order:transfer-matrix approach. Journal of Physics A:Mathematical and General.1988,21(7):1649-1677
[26]Yang Q B, Kuo H K. A new description of pentagonal Frank-Kasper phases and a possible structure model of the icosahedral quasicrystal. Acta Crystallographica 1987, A43(6):787-795
[27]Pan G Z, Cheng Y F, Li F H. Six-dimensional crystal related to T2-phase Al6CuLi3 icosahedral quasicrystal and R-phase Al5CuLi3 body-centered-cubic crystal. Physical Review B,1990,41(6):3401-3405.
[28]Pan G Z, Tang C M, Li F H. Six-dimensional crystal-structure model for i-(Al-Mn-Si) and alpha-(Al-Mn-Si). Physical Review B,1992,46(10): 6091-6098.
[29]Yamamoto A, Hiraga K. Structure of an icosahedral Al-Mn quasicrystal. Physical Review B,1988,37(11):6207-6214
[30]Ping L, Stigenberg A H, Nilsson J O. Quasicrystalline and crystalline precipitation during isothermal tempering in a 12Cr-9Ni-4Mo maraging stainless steel. Acta Metallurgica et Materialia,1995,43(7):2881-2890
[31]Tsai A P, Aoki K, Inoue A, et al. Synthesis of stable quasicrystalline particle-dispersed Al base composite alloys. Journal of Materials Research, 1993,8:5-7
[32]Bae D H, Lee M H, Kim K T, et al. Application of Quasicrystalline Particles As a Strengthening Phase in Mn-Zn-Y Alloys. Journal of Alloys and Compounds, 2002,342(1-2):445-450
[33]Moriarty J A, Widom M. First-principles interatomic potentials for transition-metal aluminides:Theory and trends across the 3d series. Physical Review B, 1997,56(13):7905-7917
[34]Widom M, Al-Lehyani Ⅰ, Moriarty J A. First-principles interatomic potentials for transition-metal aluminides. Ⅲ. Extension to ternary phase diagrams. Physical Review B,2000,62(6):3648-3657
[35]Hocker S, Gahler F. Aluminium Diffusion in Decagonal Quasicrystals. Physical Review Letters,2004,93(7):075901
[36]Ercolessi F, Adams J B. Interatomic potentials from first-principles calculations:the Force-Matching method. Europhysics Letters,1994,26(8): 583-588
[37]Hocker S, Gahler F, Brommer P. Molecular dynamics simulation of aluminium diffusion in decagonal quasicrystals. Philosophical Magazine,2006,86(6-8): 1051-1057
[38]Brommer P, Gahler F, Mihalkovic M. Ordering and correlation of cluster orientations in CaCd6. Philosophical Magazine,2007,87(18-21):2671-2677
[39]Rosch F, Trebin H R, Gunbsch P. Interatomic Potentials and the simulation of fracture:C15 NbCr2. International Journal of Fracture,2006,139(3-4):517-526
[40]Audier M, Durand-charre M, De Boissieu M. Aluminum-Palladium-Manganese Phase Diagram in the Region of Quasicrystalline Phases. Philosophical Magazine B,1993,68(5):607-618
[41]Godecke T, Luck R. The Aluminum-Palladium-Manganese System in the Range from 60 to 100 at.%Al. Zeitschrift fuer Metallkunde/Materials Research and Advanced Techniques,1995,86(2):109-121
[42]Ranganathan S, Chattopadhyay K. Quasicrystals. Annual Review of Materials Research,1991,21:437-462
[43]Yang X X, Wang R H, Fan X J. Phase transitions in A162Cu25.5Fe12.5 quasicrystal induced by low-temperature Ar2+ irradiation. Philosophical Magazine Letters,1996,73(3):121-127
[44]Wang R H, Takahashi H, Ohnuki S, Yang X X. Phase transformation induced by irradiating an A162Cu25.5Fe12.5 icosahedral quasicrystal. Journal of Physics: Condensed Matter,1995,7(10):2105-2114
[45]Wang Z G, Yang X X, Wang R H. Ar+-ion-irradiation-induced phase transformation in an A162Cu25.5Fe12.5 icosahedral quasicrystal. Journal of Physics:Condensed Matter,1993,5(41):7569-7576
[46]Wang R H, Takahashi H, Ohnuki S. Irradiation-induced amorphization of the A176Si4Mn20 icosahedral quasicrystal. Rdiation Effects and Defects in Solids, 1994,129(3-4):173-180
[47]Wang Z G, Deng W F, Wang R H. Ar+ion irradiation damage effects in A176Si4Mn20 icosahedral quasicrystals. Physica Status Solidi A,1992,133(2): 299-304
[48]Wang R H, Gui J N, Yao S N, et al. High-temperature X-ray diffraction study of the crystallization process in rapidly quenched A16(Mn, Fe) alloys. Philosophical Magazine B,1986,54(2):L33-L37
[49]Engel M, Trebin H-R. Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential. Physical Review Letters, 2007,98(22):225505
[50]Roth J, Schiling R, Trebin H-R. Stability of monatomic and diatomic quasicarystals and the influence of noise. Physical Review B,1990,41(5): 2735-2747
[51]Dong C, Zhang Q H, Wang D H, et al. Al-Cu approximants and associated B2 chemical-twinning modes. Micron,2000,31(5):507-514
[52]Dong C, Zhang Q H, Wang D H, et al. Al-Cu approximants in the A13Cu4 alloy. The European Physical Journal B,1998,6(1):25-32
[53]Duguet T, Unal B, de Weerd M C, et al. Twofold surface of the decagonal Al-Cu-Co quasicrystal. Physical Review B,2009,80(2):024201
[54]Mihalkovic M, Elhor H, Suck J B. Atomic dynamics in Al-rich Al-Co alloys near the composition of the decagonal quasicrystal. Physical Review B,2001, 63(21):214301
[55]Conrad M, Krumeich F, Reich C, et al. The mesoscopic structure of disordered dodecagonal tantalum telluride:a high-resolution transmission electron microscopy study. Philosophical Magazine Letters,1998,78(5):3577-367
[56]Krumeich F, Reich C, Conrad M, et al. Periodic and Aperiodic Arrangements of Dodecagonal (Ta,V)151Te74 Clusters Studied by Transmission Electron Microscopy-The Method's Merits and Limitations. Materials Science and Engineering:A,2000,294-296:152-155
[57]Uchida M, Horiuchi S. Modulated-Crystal Model for the Twelvefold Quasi-crystal Ta62Te38. Journal of Applied Crystallography,1998,31(4):634-637
[58]Guo J Q, Tsai A P. Stable icosahedral quasicrystals in the Ag-In-Ca, Ag-In-Yb, Ag-In-Ca-Mg and Ag-In-Yb-Mg systems. Philosophical Magazine Letters,2002, 82(6):349-352
[59]Guo J Q, Abe E, Tsai A P. A new stable icosahedral quasicrystal in the Cd-Mg-Dy system. Philosophical Magazine Letters,2001,81(1):17-21
[60]Guo J Q, Abe E, Tsai A P. Stable icosahedral quasicrystals in binary Cd-Ca and Cd-Yb systems. Physical Review B,2000,62(22):R14605-R14607
[61]Daw M S, Baske M I. Embedded-atom Method:Derivation an Application to Impurities, Surface, and Other Defects in Metals. Physical Review B,1984, 29(12):6443-6453
[62]Daw M S, Baske M I. Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals. Physical Review B,1983,50(17): 1285-1288
[63]Johnson R A. Analytic Nearest-neighbor Model for FCC Metals. Physical Review B,1989,37(12):3924-3931
[64]Johnson R A. Alloy models with the embedded-atom method. Physical Review B,1989,39(17):12554-12559
[65]Johnson R A. Phase stability of fcc alloys with the embedded-atom method. Physical Review B,1990,41(14):9717-9720
[66]张邦维,胡望宇,舒小林.嵌入原子方法理论及其在材料科学中的应用—原子尺度材料设让理论.长沙：湖南大学出版社,2003,245-256
[67]Hu W Y, Zhang B W, Huang B Y, et al. Analytic Modified Embedded Atom Potentials for HCP Metals. Journal of Physics:Condensed Matter,2001,13(6): 1193-1213
[68]Hu W Y, Masahiro F. The Application of the Analytic Embedded Atom Potentials to Alkali Metals. Modeling and Simulation in Science, Engineering and Technology,2002,10(6):707-726
[69]Zhang B W. Application of Miedema coordinates to the formation of binary amorphous-alloys. Physica B&C,1983,121(3):405-408
[70]Zhang B W. Description of the formation of binary amorphous-alloys by chemical coordinates. Physica B&C,1985,132(3):319-332
[71]Zhang B W. Semi-empirical theory of solid solubility in binary-alloys. Zeitschrift fuer Metallkunde/Materials Research and Advanced Techniques, 1985,76(4):264-270
[72]Zhang B W. A semiempirical approach to the prediction of the amprphous-alloys formed by ion-beam mixing. physica status solidi A,1987,102(1): 199-206
[73]Heerman D W. Computer Simulations Methods in Theoretical Physics. Berlin: Springer-Verlag,1990,87-95
[74]Berndt R, Lock A, Woll C. Computer algebra approach to surface lattice dynamics. Surface Science,1992,276(1-3):213-225
[75]Ozgen S, Duruk E, Molecular dynamics simulation of solidification kinetics of aluminium using Sutton-Chen version of EAM. Materials Letters,2004,58(6): 1071-1075
[76]Alder B J, Wairiwright T E. Phase Transition for a Hard-sphere System. Journal of Chemical Physics,1957,27(5):1208-1209
[77]Anderson H C. Molecular Dynamics Simulations at Constant Press and/or Temperature. Journal of Chemical Physics,72(4):2384-2393
[78]Parrinello M, Rahman A. Crystal structure and Pair Potentials:A Molecular Dynamics Study. Physical Review Letters,1980,45(14):1196-1199
[79]Verlet L. Computer‘Experiments’on Classical Fluids I Thermodynamical Properties of Lennard-Jones Molecules. Physical Review,1967,159(1):98-103
[80]Honeycutt R W. The potential Calculation and Some Applications. Methods in Computational Physics,1970,9(2):136-211
[81]Gear C W. Numerical Initial Value Problems in Ordinary Differential Equation. NJ:Prentice-Hall PTR,1971,132-138
[82]Berendsen H J C, Postma J P M, Gunsteren W F V. Molecular dynamics with coupling to an external bath. Journal of Chemical Physics,1984,81(8): 3684-3690
[83]Hoover W G. Computational Statistical Mechamics. New York:Elsevier,1991, 121-128
[84]Andrew R L. Molecular Modeling:Principle and Practice. Berlin Herdelberg: Springer-Verlag,1996,357-359
[85]Honeycutt J D, Andersen H C. Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. The Journal of Physical Chemistry, 1987,91(19):4950-4963
[86]胡壮麒,王鲁红,刘轶事.电子和原子层次材料行为的计算机模拟.材料研究学报,1998,12(1)：1-19
[87]Steinhardt P J, Nelson D R, Ronchetti M. Bond-orientational order in liquids and glasses. Physical Review B,1983,28(2):784-805
[88]Sankaranarayanan S K R S, Bhethanabotla V R, Joseph B. Molecular dynamics simulation study of the melting of Pd-Pt nanoclusters. Physical Review B, 2005, 71(19):195415
[89]Qin Y L, Wang R H, Wang Q L, et al. Ar-ion-irradiation-induced phase transformations in an Al70Co15Ni15 decagonal quasicrystal. Philosophical Magazine Letters,1995,71(2):83-90
[90]Lubensky T C, Socolar J E S, Steinbardt P J, et al. Distortion and Peak Broadening in Quasicrystal Diffraction Patterns. Physical Review Letters,1986, 57(2):1440-1443
[91]Zhang H, Uban K. Radiation-induced transfortmation from the decagonal quasicrystalline phase to a CsCl-type phase in Al-Cu-Co(-Si). Philosophical Magazine Letters,1992,66(4):209-215
[92]He Y, Chen H, Meng X F, et al. Stability investigation of a decagonal Al-Cu-Co quasicrystal. Philosophical Magazine Letters,1991,63(4):211-216
[93]Mayer J, Uban K, Fidler J. Phase transitions between the quasicrystals, crystalline, and amorphous phases in Al-16at%V. Physica Status Solidi A,1987, 99:467-473
[94]Uban K, Morser N, Kronmuller H. Phase reansitions between the quasi-crystalline crystalline, and amorphous phase in Al-14at%Mn. Physica Status. Solidi A,1985,91:411-422
[95]Pan G Z, Cheng Y F, Li F H. Six-dimensional crystal related to T2-phase A16CuLi3 icosahedral quasicrystal and R-phase A15CuLi3 body-centered-cubic crystal. Physical Review B,1990,41(6):3401-3405
[96]Pan G Z, Teng M C, Li F H. Six-dimensional crystal-structure model for i-(Al-Mn-Si) and a-(Al-Mn-Si). Physical Review B,1992,46(10):6091-6098
[97]Dzugutov M. Glass formation in a monatomic liquid with icosahedral inherent local order. Physical Review A,1992,46(6):R2984-R2987
[98]郑子樵.材料科学基础.长沙：中南大学出版社,2005,67-68
[99]Curran D R, Seaman L, Shockey D A. Dynamic filure of solids. Physics reports, 1987,147(5-6):253-388
[100]哈宽富.金属力学性质的微观理论.北京：科学出版社,1991,457-460
[101]张俊善.材料强度学.哈尔滨：哈尔滨工业大学出版社,2004,107-109
[102]Ikeda H, Qi Y, Cagin T, et al. Strain rate induced amorphization in metallic nanowires. Physical Review Letters,1999,82(14):2900-2903
[103]Branicio P S, Rino J P. Large deformation and amorphization of Ni nanowires under uniaxial strain:a molecular dynamics study. Physical Review B,2000, 62(24):16950-16955
[104]文玉华,周富信,刘曰武.纳米晶铜单向拉伸变形的分子动力学模拟.力学学报,2002,34(1)：29-36
[105]徐洲,王秀喜,梁海弋.铜纳米丝的应变率和尺寸效应的分子动力学模拟.材料研究学报,2003,6(17)：262-267
[106]王海龙,王秀喜,梁海弋.分子动力学模拟金属玻璃Cu应力晶化的应变率效应..材料研究学报.2006,10(20)：474-478
[107]Mabuchi M. Low temperature superplasticity of Az91 alloy with on-equilibrium grain boundaries. Acta Materialia,1999,47(7):2047-2051
[108]Watanabe H, Mukai T, Ishikawa K. High-strain-rate superplasticity at low temperature in a ZK61 alloy produced by powder metallurgy. Scripta Materialia, 1999,41(2):209-213
[109]Duneau M, Katz A. Quasiperiodic Patterns. Physical Review Letters,1985, 54(25):2688-2691
[110]田鹤.复杂结构合金相中特殊缺陷的显微结构研究：[中国科学院博士学位论文].北京：中国科学院物理研究所,2006：30-32
[111]Dzugutov M, Simdyankin S I, Zetterling F H. Decoupling of Diffusion from Structural Relaxation and Spatial Heterogeneity in a Supercooled Simple Liquid. Physical Review Letters,2002,89(19):195801
[112]Simdyankin S I, Dzugutov M, Taraskin S N, et al. Connection between vibrational dynamics and topological order in simple glasses. Physical Review B,2001,63(18):184301
[113]Engel M, Trebin H-R. Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential. Physical Review Letters,2007,98(22):225505
[114]De Boissieu M, Francoual S, Mihalkovic, et al. Lattice dynamics of the Zn-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic 1/1 approximant. Nature Materials,2007,6:977-984
[2]Levine D, Steinhardt P J. Quasicrystals:A new class of ordered structures. Physical Review Letters,1984,53(26):2477-2480
[3]Penrose R. Pentaplexity. Eureka,1978,39:16-22
[4]Penrose R. The role of aesthetics in pure and applied mathematical research. Bulletin of the Institute of Mathematics and its Applications,1974,10:266-271
[5]Elser V. Indexing problems in quasicrystal diffraction. Physical Review B,1985, 32(8):4892-4898
[6]Katz A, Duneau M. Quasiperiodic patterns and icosahedral symmetry. Journal of Physical France.1986,47(2):181-196
[7]Gahler F, Gummelt P, Ben-Abraham S I. Generation of quasiperiodic order by maximal cluster covering, in Coverings of Discrete Quasiperiodic Sets:Theory and Applications to Quasicrystals. Berlin:Springer,2002,63-93
[8]Ben-Abraham S I, Gummelt P, Luck R, et al. Dodecagonal tilings almost covered by a single cluster. Ferroelectrics,2001,250(1-4):313-316
[9]Gahler F, Luck R, Ben-Abraham S I, et al. Dodecagonal tilings as maximal cluster coverings. Ferroelectrics,2001,250(1-4):335-338
[10]Gummelt P, Bandt C. A cluster approach to random Penrose tilings. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing,2000,294-296:250-253
[11]Puellmann K, Gummelt I, Kadar J, et al. Apoptosis of normal and G-CSF induced cells:Influences of pentoxifylline and amifostine. Journal of Leukocyte Biology,1998,48:178-183
[12]Gummelt P. Penrose tilings as coverings of congruent decagons. Geometriae Dedicata,1996,62(1):1-17
[13]Schechtman D, Blech I A. The microstructure of rapidly solidified A16Mn. Metallurgical and Materials Transactions A,1985,16(6):1005-1012
[14]Stephens P W, Goldman A I. Sharp Diffraction Maxima from an Icosahedral Glass. Physical Review Letters,1986,56(17):1168-1171
[15]Widom M, Strandgurg K, Swenden R H. Quasicrystal equilibrium state. Physical Review Letters,1987,58(7):706-709
[16]Janssen T. In Quasicrystals, Proceedings of the Adriatico Research Conference. Edited by Jaric and S. Lundquist. Singapore:World Scientific,1990,337-341
[17]Elser V. Comment on Quasicrystals:A New Class of Ordered Structures. Physical Review Letters,1985,54(15):1730-1733
[18]Strandburg K. Random-tiling quasicrystal. Physical Review B,1989,40(9): 6071-6084
[19]Pauling L. Apparent icosaedral symmetry is due to directed multiple twinning of cubic crystals. Nature,1985,317:512-514
[20]Pauling L. So-called icosahedral and decagonal quasicrysatls are twins of an 820-atom cubic crystal. Physical Review Letters,1987,58(4):365-368
[21]Henley C, Elser V. Quasicrystal structure of (Al,Zn)49Mg32. Philosophical Magazine B,1986,53(3):L59-L66
[22]Guyot P, Audier M. A quasicrystal structure model for AI-Mn. Philosophical Magazine B,1985,52(1):L15-L19
[23]Audier M, Guyot P. A perfect icosahedral atomic structure:A two-unit-cell and four-zonohedra description. Philosophical Magazine Letters,1988,58(1):17-23
[24]Elser V. XVth International Colloquiumon Groupn Theoretical Methods in Physics, edited by R. Gilmore. Singapore:World Scientific,1987,330-334
[25]Henley C L. Random tilings with quasicrystal order:transfer-matrix approach. Journal of Physics A:Mathematical and General.1988,21(7):1649-1677
[26]Yang Q B, Kuo H K. A new description of pentagonal Frank-Kasper phases and a possible structure model of the icosahedral quasicrystal. Acta Crystallographica 1987, A43(6):787-795
[27]Pan G Z, Cheng Y F, Li F H. Six-dimensional crystal related to T2-phase Al6CuLi3 icosahedral quasicrystal and R-phase Al5CuLi3 body-centered-cubic crystal. Physical Review B,1990,41(6):3401-3405.
[28]Pan G Z, Tang C M, Li F H. Six-dimensional crystal-structure model for i-(Al-Mn-Si) and alpha-(Al-Mn-Si). Physical Review B,1992,46(10): 6091-6098.
[29]Yamamoto A, Hiraga K. Structure of an icosahedral Al-Mn quasicrystal. Physical Review B,1988,37(11):6207-6214
[30]Ping L, Stigenberg A H, Nilsson J O. Quasicrystalline and crystalline precipitation during isothermal tempering in a 12Cr-9Ni-4Mo maraging stainless steel. Acta Metallurgica et Materialia,1995,43(7):2881-2890
[31]Tsai A P, Aoki K, Inoue A, et al. Synthesis of stable quasicrystalline particle-dispersed Al base composite alloys. Journal of Materials Research, 1993,8:5-7
[32]Bae D H, Lee M H, Kim K T, et al. Application of Quasicrystalline Particles As a Strengthening Phase in Mn-Zn-Y Alloys. Journal of Alloys and Compounds, 2002,342(1-2):445-450
[33]Moriarty J A, Widom M. First-principles interatomic potentials for transition-metal aluminides:Theory and trends across the 3d series. Physical Review B, 1997,56(13):7905-7917
[34]Widom M, Al-Lehyani Ⅰ, Moriarty J A. First-principles interatomic potentials for transition-metal aluminides. Ⅲ. Extension to ternary phase diagrams. Physical Review B,2000,62(6):3648-3657
[35]Hocker S, Gahler F. Aluminium Diffusion in Decagonal Quasicrystals. Physical Review Letters,2004,93(7):075901
[36]Ercolessi F, Adams J B. Interatomic potentials from first-principles calculations:the Force-Matching method. Europhysics Letters,1994,26(8): 583-588
[37]Hocker S, Gahler F, Brommer P. Molecular dynamics simulation of aluminium diffusion in decagonal quasicrystals. Philosophical Magazine,2006,86(6-8): 1051-1057
[38]Brommer P, Gahler F, Mihalkovic M. Ordering and correlation of cluster orientations in CaCd6. Philosophical Magazine,2007,87(18-21):2671-2677
[39]Rosch F, Trebin H R, Gunbsch P. Interatomic Potentials and the simulation of fracture:C15 NbCr2. International Journal of Fracture,2006,139(3-4):517-526
[40]Audier M, Durand-charre M, De Boissieu M. Aluminum-Palladium-Manganese Phase Diagram in the Region of Quasicrystalline Phases. Philosophical Magazine B,1993,68(5):607-618
[41]Godecke T, Luck R. The Aluminum-Palladium-Manganese System in the Range from 60 to 100 at.%Al. Zeitschrift fuer Metallkunde/Materials Research and Advanced Techniques,1995,86(2):109-121
[42]Ranganathan S, Chattopadhyay K. Quasicrystals. Annual Review of Materials Research,1991,21:437-462
[43]Yang X X, Wang R H, Fan X J. Phase transitions in A162Cu25.5Fe12.5 quasicrystal induced by low-temperature Ar2+ irradiation. Philosophical Magazine Letters,1996,73(3):121-127
[44]Wang R H, Takahashi H, Ohnuki S, Yang X X. Phase transformation induced by irradiating an A162Cu25.5Fe12.5 icosahedral quasicrystal. Journal of Physics: Condensed Matter,1995,7(10):2105-2114
[45]Wang Z G, Yang X X, Wang R H. Ar+-ion-irradiation-induced phase transformation in an A162Cu25.5Fe12.5 icosahedral quasicrystal. Journal of Physics:Condensed Matter,1993,5(41):7569-7576
[46]Wang R H, Takahashi H, Ohnuki S. Irradiation-induced amorphization of the A176Si4Mn20 icosahedral quasicrystal. Rdiation Effects and Defects in Solids, 1994,129(3-4):173-180
[47]Wang Z G, Deng W F, Wang R H. Ar+ion irradiation damage effects in A176Si4Mn20 icosahedral quasicrystals. Physica Status Solidi A,1992,133(2): 299-304
[48]Wang R H, Gui J N, Yao S N, et al. High-temperature X-ray diffraction study of the crystallization process in rapidly quenched A16(Mn, Fe) alloys. Philosophical Magazine B,1986,54(2):L33-L37
[49]Engel M, Trebin H-R. Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential. Physical Review Letters, 2007,98(22):225505
[50]Roth J, Schiling R, Trebin H-R. Stability of monatomic and diatomic quasicarystals and the influence of noise. Physical Review B,1990,41(5): 2735-2747
[51]Dong C, Zhang Q H, Wang D H, et al. Al-Cu approximants and associated B2 chemical-twinning modes. Micron,2000,31(5):507-514
[52]Dong C, Zhang Q H, Wang D H, et al. Al-Cu approximants in the A13Cu4 alloy. The European Physical Journal B,1998,6(1):25-32
[53]Duguet T, Unal B, de Weerd M C, et al. Twofold surface of the decagonal Al-Cu-Co quasicrystal. Physical Review B,2009,80(2):024201
[54]Mihalkovic M, Elhor H, Suck J B. Atomic dynamics in Al-rich Al-Co alloys near the composition of the decagonal quasicrystal. Physical Review B,2001, 63(21):214301
[55]Conrad M, Krumeich F, Reich C, et al. The mesoscopic structure of disordered dodecagonal tantalum telluride:a high-resolution transmission electron microscopy study. Philosophical Magazine Letters,1998,78(5):3577-367
[56]Krumeich F, Reich C, Conrad M, et al. Periodic and Aperiodic Arrangements of Dodecagonal (Ta,V)151Te74 Clusters Studied by Transmission Electron Microscopy-The Method's Merits and Limitations. Materials Science and Engineering:A,2000,294-296:152-155
[57]Uchida M, Horiuchi S. Modulated-Crystal Model for the Twelvefold Quasi-crystal Ta62Te38. Journal of Applied Crystallography,1998,31(4):634-637
[58]Guo J Q, Tsai A P. Stable icosahedral quasicrystals in the Ag-In-Ca, Ag-In-Yb, Ag-In-Ca-Mg and Ag-In-Yb-Mg systems. Philosophical Magazine Letters,2002, 82(6):349-352
[59]Guo J Q, Abe E, Tsai A P. A new stable icosahedral quasicrystal in the Cd-Mg-Dy system. Philosophical Magazine Letters,2001,81(1):17-21
[60]Guo J Q, Abe E, Tsai A P. Stable icosahedral quasicrystals in binary Cd-Ca and Cd-Yb systems. Physical Review B,2000,62(22):R14605-R14607
[61]Daw M S, Baske M I. Embedded-atom Method:Derivation an Application to Impurities, Surface, and Other Defects in Metals. Physical Review B,1984, 29(12):6443-6453
[62]Daw M S, Baske M I. Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals. Physical Review B,1983,50(17): 1285-1288
[63]Johnson R A. Analytic Nearest-neighbor Model for FCC Metals. Physical Review B,1989,37(12):3924-3931
[64]Johnson R A. Alloy models with the embedded-atom method. Physical Review B,1989,39(17):12554-12559
[65]Johnson R A. Phase stability of fcc alloys with the embedded-atom method. Physical Review B,1990,41(14):9717-9720
[66]张邦维,胡望宇,舒小林.嵌入原子方法理论及其在材料科学中的应用—原子尺度材料设让理论.长沙：湖南大学出版社,2003,245-256
[67]Hu W Y, Zhang B W, Huang B Y, et al. Analytic Modified Embedded Atom Potentials for HCP Metals. Journal of Physics:Condensed Matter,2001,13(6): 1193-1213
[68]Hu W Y, Masahiro F. The Application of the Analytic Embedded Atom Potentials to Alkali Metals. Modeling and Simulation in Science, Engineering and Technology,2002,10(6):707-726
[69]Zhang B W. Application of Miedema coordinates to the formation of binary amorphous-alloys. Physica B&C,1983,121(3):405-408
[70]Zhang B W. Description of the formation of binary amorphous-alloys by chemical coordinates. Physica B&C,1985,132(3):319-332
[71]Zhang B W. Semi-empirical theory of solid solubility in binary-alloys. Zeitschrift fuer Metallkunde/Materials Research and Advanced Techniques, 1985,76(4):264-270
[72]Zhang B W. A semiempirical approach to the prediction of the amprphous-alloys formed by ion-beam mixing. physica status solidi A,1987,102(1): 199-206
[73]Heerman D W. Computer Simulations Methods in Theoretical Physics. Berlin: Springer-Verlag,1990,87-95
[74]Berndt R, Lock A, Woll C. Computer algebra approach to surface lattice dynamics. Surface Science,1992,276(1-3):213-225
[75]Ozgen S, Duruk E, Molecular dynamics simulation of solidification kinetics of aluminium using Sutton-Chen version of EAM. Materials Letters,2004,58(6): 1071-1075
[76]Alder B J, Wairiwright T E. Phase Transition for a Hard-sphere System. Journal of Chemical Physics,1957,27(5):1208-1209
[77]Anderson H C. Molecular Dynamics Simulations at Constant Press and/or Temperature. Journal of Chemical Physics,72(4):2384-2393
[78]Parrinello M, Rahman A. Crystal structure and Pair Potentials:A Molecular Dynamics Study. Physical Review Letters,1980,45(14):1196-1199
[79]Verlet L. Computer‘Experiments’on Classical Fluids I Thermodynamical Properties of Lennard-Jones Molecules. Physical Review,1967,159(1):98-103
[80]Honeycutt R W. The potential Calculation and Some Applications. Methods in Computational Physics,1970,9(2):136-211
[81]Gear C W. Numerical Initial Value Problems in Ordinary Differential Equation. NJ:Prentice-Hall PTR,1971,132-138
[82]Berendsen H J C, Postma J P M, Gunsteren W F V. Molecular dynamics with coupling to an external bath. Journal of Chemical Physics,1984,81(8): 3684-3690
[83]Hoover W G. Computational Statistical Mechamics. New York:Elsevier,1991, 121-128
[84]Andrew R L. Molecular Modeling:Principle and Practice. Berlin Herdelberg: Springer-Verlag,1996,357-359
[85]Honeycutt J D, Andersen H C. Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. The Journal of Physical Chemistry, 1987,91(19):4950-4963
[86]胡壮麒,王鲁红,刘轶事.电子和原子层次材料行为的计算机模拟.材料研究学报,1998,12(1)：1-19
[87]Steinhardt P J, Nelson D R, Ronchetti M. Bond-orientational order in liquids and glasses. Physical Review B,1983,28(2):784-805
[88]Sankaranarayanan S K R S, Bhethanabotla V R, Joseph B. Molecular dynamics simulation study of the melting of Pd-Pt nanoclusters. Physical Review B, 2005, 71(19):195415
[89]Qin Y L, Wang R H, Wang Q L, et al. Ar-ion-irradiation-induced phase transformations in an Al70Co15Ni15 decagonal quasicrystal. Philosophical Magazine Letters,1995,71(2):83-90
[90]Lubensky T C, Socolar J E S, Steinbardt P J, et al. Distortion and Peak Broadening in Quasicrystal Diffraction Patterns. Physical Review Letters,1986, 57(2):1440-1443
[91]Zhang H, Uban K. Radiation-induced transfortmation from the decagonal quasicrystalline phase to a CsCl-type phase in Al-Cu-Co(-Si). Philosophical Magazine Letters,1992,66(4):209-215
[92]He Y, Chen H, Meng X F, et al. Stability investigation of a decagonal Al-Cu-Co quasicrystal. Philosophical Magazine Letters,1991,63(4):211-216
[93]Mayer J, Uban K, Fidler J. Phase transitions between the quasicrystals, crystalline, and amorphous phases in Al-16at%V. Physica Status Solidi A,1987, 99:467-473
[94]Uban K, Morser N, Kronmuller H. Phase reansitions between the quasi-crystalline crystalline, and amorphous phase in Al-14at%Mn. Physica Status. Solidi A,1985,91:411-422
[95]Pan G Z, Cheng Y F, Li F H. Six-dimensional crystal related to T2-phase A16CuLi3 icosahedral quasicrystal and R-phase A15CuLi3 body-centered-cubic crystal. Physical Review B,1990,41(6):3401-3405
[96]Pan G Z, Teng M C, Li F H. Six-dimensional crystal-structure model for i-(Al-Mn-Si) and a-(Al-Mn-Si). Physical Review B,1992,46(10):6091-6098
[97]Dzugutov M. Glass formation in a monatomic liquid with icosahedral inherent local order. Physical Review A,1992,46(6):R2984-R2987
[98]郑子樵.材料科学基础.长沙：中南大学出版社,2005,67-68
[99]Curran D R, Seaman L, Shockey D A. Dynamic filure of solids. Physics reports, 1987,147(5-6):253-388
[100]哈宽富.金属力学性质的微观理论.北京：科学出版社,1991,457-460
[101]张俊善.材料强度学.哈尔滨：哈尔滨工业大学出版社,2004,107-109
[102]Ikeda H, Qi Y, Cagin T, et al. Strain rate induced amorphization in metallic nanowires. Physical Review Letters,1999,82(14):2900-2903
[103]Branicio P S, Rino J P. Large deformation and amorphization of Ni nanowires under uniaxial strain:a molecular dynamics study. Physical Review B,2000, 62(24):16950-16955
[104]文玉华,周富信,刘曰武.纳米晶铜单向拉伸变形的分子动力学模拟.力学学报,2002,34(1)：29-36
[105]徐洲,王秀喜,梁海弋.铜纳米丝的应变率和尺寸效应的分子动力学模拟.材料研究学报,2003,6(17)：262-267
[106]王海龙,王秀喜,梁海弋.分子动力学模拟金属玻璃Cu应力晶化的应变率效应..材料研究学报.2006,10(20)：474-478
[107]Mabuchi M. Low temperature superplasticity of Az91 alloy with on-equilibrium grain boundaries. Acta Materialia,1999,47(7):2047-2051
[108]Watanabe H, Mukai T, Ishikawa K. High-strain-rate superplasticity at low temperature in a ZK61 alloy produced by powder metallurgy. Scripta Materialia, 1999,41(2):209-213
[109]Duneau M, Katz A. Quasiperiodic Patterns. Physical Review Letters,1985, 54(25):2688-2691
[110]田鹤.复杂结构合金相中特殊缺陷的显微结构研究：[中国科学院博士学位论文].北京：中国科学院物理研究所,2006：30-32
[111]Dzugutov M, Simdyankin S I, Zetterling F H. Decoupling of Diffusion from Structural Relaxation and Spatial Heterogeneity in a Supercooled Simple Liquid. Physical Review Letters,2002,89(19):195801
[112]Simdyankin S I, Dzugutov M, Taraskin S N, et al. Connection between vibrational dynamics and topological order in simple glasses. Physical Review B,2001,63(18):184301
[113]Engel M, Trebin H-R. Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential. Physical Review Letters,2007,98(22):225505
[114]De Boissieu M, Francoual S, Mihalkovic, et al. Lattice dynamics of the Zn-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic 1/1 approximant. Nature Materials,2007,6:977-984